# Given a set of candidate numbers (candidates) (without duplicates) and a target number (target), 
# find all unique combinations in candidates where the candidate numbers sums to target.

# The same repeated number may be chosen from candidates unlimited number of times.

# Note:

# All numbers (including target) will be positive integers.
# The solution set must not contain duplicate combinations.
# Example 1:

# Input: candidates = [2,3,6,7], target = 7,
# A solution set is:
# [
#   [7],
#   [2,2,3]
# ]
# Example 2:

# Input: candidates = [2,3,5], target = 8,
# A solution set is:
# [
#   [2,2,2,2],
#   [2,3,3],
#   [3,5]
# ]


class Solution:
    def combinationSum_(self, candidates, target):
        candidates.sort()
        out_list = []
        def dfs(target,index,list_to_save):

            if target < 0:
                return
            if target ==0:
                out_list.append(list_to_save)
                return
            for i in range(index,len(candidates)):
                dfs(target - candidates[i],index=i,list_to_save = list_to_save + [candidates[i]])
        dfs(target,index=0,list_to_save=[])
        return out_list

    def combinationSum(self, candidates, target):
        res = []
        candidates.sort()
        self.dfs(candidates, target, 0, [], res)
        return res
        
    def dfs(self, nums, target, index, path, res):
        if target < 0:
            return  # backtracking
        if target == 0:
            res.append(path)
            return 
        for i in range(index, len(nums)):
            self.dfs(nums, target-nums[i], i, path+[nums[i]], res)



if __name__ == "__main__":
    candi = [5,2,1,2,3,3]
    t = 8
    out_list = Solution().combinationSum_(candi,t)
    for item in out_list:
        print(item)